   Chapter 5, Problem 24RE ### Calculus: An Applied Approach (Min...

10th Edition
Ron Larson
ISBN: 9781305860919

#### Solutions

Chapter
Section ### Calculus: An Applied Approach (Min...

10th Edition
Ron Larson
ISBN: 9781305860919
Textbook Problem
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# Applying the General Power Rule In Exercises 21–32, find the indefinite integral. Check your result by differentiating. ∫ ( 4 x 3 + 2 ) x 4 + 2 x   d x

To determine

To calculate: The indefinite integral (4x3+2)(x4+2x)dx.

Explanation

Given Information:

The provided indefinite integral is (4x3+2)(x4+2x)dx.

Formula used:

The power rule of integrals:

undu=un+1n+1+C (n1)

The power rule of differentiation:

ddxun=nun1+C

Calculation:

Consider the indefinite integral:

(4x3+2)(x4+2x)dx

Let u=x4+2x, then derivative will be,

du=d(x4+2x)=(4x3+2)dx

Substitute du for (4x3+2)dx and u for x4+2x in provided integration.

(4x3+2)(x4+2x)dx=udu

Now apply, the power rule of integrals:

udu=u1/2+112+1+C=2

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